Search: id:A098503
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%I A098503
%S A098503 1,2,3,4,20,15,8,84,210,105,16,288,1512,2520,945,32,880,7920,27720,
%T A098503 34650,10395,64,2496,34320,205920,540540,540540,135135,128,6720,131040,
%U A098503 1201200,5405400,11351340,9459450,2027025,256,17408
%V A098503 1,-2,3,4,-20,15,-8,84,-210,105,16,-288,1512,-2520,945,-32,880,-7920,27720,
               -34650,
%W A098503 10395,64,-2496,34320,-205920,540540,-540540,135135,-128,6720,-131040,
               1201200,-5405400,
%X A098503 11351340,-9459450,2027025,256,-17408
%N A098503 Triangle T(n,k) by rows: coefficients of 2^n * L(n,1/2,x), with L the 
               generalized Laguerre polynomials.
%F A098503 T(n, k) = (-2)^n * n!/k! * C(n+1/2, n-k), n>=0, k<=n.
%e A098503 2^0 L(0,1/2,x) = 1.
%e A098503 2^1 L(1,1/2,x) = -2*x + 3.
%e A098503 2^2 L(2,1/2,x) = 4*x^2 - 20*x + 15.
%e A098503 2^3 L(3,1/2,x) = -8*x^3 + 84*x^2 - 210*x + 105.
%e A098503 2^4 L(4,1/2,x) = 16*x^4 - 288*x^3 + 1512*x^2 - 2520*x + 945.
%Y A098503 Columns include (-1)^n times A000079, n/2*A014480. Diagonals include 
               A001147, -A000906, 4*A001881.
%Y A098503 Sequence in context: A058772 A012285 A012281 this_sequence A092974 A058186 
               A024632
%Y A098503 Adjacent sequences: A098500 A098501 A098502 this_sequence A098504 A098505 
               A098506
%K A098503 sign,tabl
%O A098503 0,2
%A A098503 Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 15 2004

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